Aircraft generally include a vertical stabilizer, which may be attached to a tail portion, or region, of the aircraft and may be utilized to provide side-to-side stability to the aircraft. The vertical stabilizer may include a composite panel, which may define a vertical tail cap that defines a leading top corner of the vertical stabilizer. The location and shape of the composite panel dictate that, during operation of the aircraft, wind, pressure, and/or drag forces exerted on the composite panel may be quite large. Thus, the composite panel must be structurally robust. However, the composite panel also may be utilized to house and/or to contain an aircraft antenna, and electromagnetic waves emitted or received by the antenna may travel through the composite panel. Under these conditions, it may be desirable to decrease an amount of material that the electromagnetic waves must pass through, as they travel through the composite panel, in order to decrease electromagnetic interference for the aircraft antenna. These two factors may compete against one another, with structural requirements dictating the use of more and/or thicker materials for the composite panel, while electromagnetic interference (EMI) requirements dictate less and/or thinner materials to maximize the performance and efficiency of the antenna signals. Thus, there exists a need for improved core structures for improved core structures for composite panels of an aircraft, for composite panels, and aircraft that include the core structures, and/or for methods of manufacturing composite panels.